A 6 meter wide pathway has been constructed along the periphery and inside of a square field of length 50 meter. The total expenditure to cover this pathway with red sand at the rate of Rs. 30 per square meter, is :

Question

Accepted Answer

To determine the total expenditure for covering the pathway with red sand, we need to calculate the area of the pathway and then multiply it by the cost per square meter.

1. **Calculate the area of the square field:**
   - The side length of the square field is 50 meters.
   - Area of the square field = side × side = 50 m × 50 m = 2500 square meters.

2. **Calculate the area of the inner square (excluding the pathway):**
   - Since the pathway is constructed along the periphery and inside the field, the inner square will have its side reduced by twice the width of the pathway (6 meters on each side).
   - Side length of the inner square = 50 m - 2 × 6 m = 38 meters.
   - Area of the inner square = 38 m × 38 m = 1444 square meters.

3. **Calculate the area of the pathway:**
   - Area of the pathway = Area of the outer square (field) - Area of the inner square.
   - Area of the pathway = 2500 square meters - 1444 square meters = 1056 square meters.

4. **Calculate the total expenditure:**
   - Cost per square meter = Rs. 30.
   - Total expenditure = Area of the pathway × Cost per square meter = 1056 square meters × Rs. 30/square meter = Rs. 31680.

Therefore, the total expenditure to cover the pathway with red sand is Rs. 31680, which corresponds to Option 3.

**Explanation for why other options are incorrect:**

- **Option 1: Rs. 75000** - This option is incorrect because it overestimates the cost. The calculated area of the pathway and the cost per square meter do not support this high expenditure.

- **Option 2: Rs. 58080** - This option is incorrect as it also overestimates the cost. The correct calculation based on the area and cost per square meter results in a lower expenditure.

- **Option 4: Rs. 1080** - This option is incorrect because it significantly underestimates the cost. Given the area of the pathway and the cost per square meter, the expenditure cannot be this low.

Thus, the correct answer is Option 3: Rs. 31680.